The preceding inequality shows that \(\rho \)  is bounded above by the Euclidean norm up to a multiplicative constant. By the inequality in [1]}, we have
\(N(\epsilon ,\mathcal {X},\rho )\le N\left((C^{-1}\sqrt{n}\epsilon /\hat{\kappa }_{01})^{2},\mathcal {X},\Vert \cdot \Vert \right)\lesssim \left(\frac{1}{(\sqrt{n}\epsilon /\hat{\kappa }_{01})^{2}}\right)^d.\) 
